4 hamburger buns or brioche rolls, split and toasted
Directions:
Pulse onion and mushrooms in a food processor until finely chopped. Heat 2 tablespoons oil in a 10-inch heavy skillet over medium heat until it shimmers. Add mushroom mixture, 3/4 teaspoon salt, and rounded 1/4 teaspoon pepper and cook, stirring occasionally, until vegetables begin to brown and liquid has evaporated, 8 to 10 minutes. Transfer to a bowl and cool to warm, stirring occasionally, about 15 minutes.
Meanwhile, cut celery and apple into 2-inch-long thin julienne with slicer.
Whisk together mayonnaise, vinegar, oil, mustard, sugar, rounded 1/8 teaspoon salt, and 1/8 teaspoon pepper in a medium bowl. Add celery and apple, tossing to coat. Let stand 15 minutes to develop flavors.
Mix buffalo into cooled mushroom mixture with your hands until well combined. Form into 4 (4-inch) patties. Heat remaining 2 teaspoons oil in a 12-inch heavy skillet over medium-high heat until it shimmers. Cook burgers, turning once, about 8 minutes total for medium-rare. Pay attention, since buffalo meat is not as fatty as ground beef, it is not as forgiving to overcooking.